"He was in such bad shape that almost immediately the guards at Ngawha transferred him to Whangarei Hospital where he subsequently passed away," Mr Davis said.
It is believed Mr Davis was referring to a case in May, in which an unnamed, 25-year-old prisoner was reported to have died after contracting a superbug.
READ MORE: Deadly bug likely to have been carried from prison
The Labour MP questioned how the bug could have given the inmate a punctured lung, which was usually an injury caused by high-speed car crashes.
He claimed that the injury came from extreme violence suffered at the Serco-run prison.
"I'm told on good authority that there is a practice in Mt Eden Correctional Facility that is called 'dropping', where ... new prisoners ... are sized up by gangs, they're bashed up, and they're dropped off the balconies onto the concrete below for good measure.
"That's what happened to prisoner Evans. He was dropped off the balcony, his lung was ruptured, but then he was transferred out of Mt Eden Correctional Facility and sent north to Ngawha."
Mr Davis also cited another case in which an inmate was transferred to a Whanganui prison with two broken legs after being dropped off a landing at the Mt Eden prison.
He urged the minister to explain the injuries.
"People are dying because of Serco. We can't under-estimate the damage and the danger."
Mr Lotu-Iiga angrily accused Mr Davis of repeating hearsay, making false allegations, and defaming the minister with comments he had made earlier this week about violence at the Mt Eden prison.
He said Mr Davis had politicised the deaths of the prisoner named Evans.
"I say to that member, shame on him," he said.
He went on: "I say to that member, put up some evidence or shut up. You're a good guy, Kelvin, but if you don't have any evidence around those defamatory statements, put up or shut up."
Mr Lotu-Iiga defended Serco's performance by saying that prisoner-on-prisoner assaults were higher in publicly-managed prisons and that contraband smuggling was a nationwide problem.
In league tables compiled by Corrections, Mt Eden was the only jail ranked as "exceptional", despite managing 30,000 movements a year as part of its remand services, he said.
Addressing claims of understaffing, he said he had been given an undertaking that Mt Eden was "fully staffed".
"But I've put Serco on notice ... that they need to improve," he said. "Clearly from the images that were transmitted across this country last week, things need to improve."
The Corrections Department is now reviewing the levels of violence and contraband smuggling in all of New Zealand's prisons.
Mr Davis said Serco should never have been given the right to run jails in New Zealand given the company's patchy record in the United Kingdom.
"We believe that the act of taking away someone's liberty and their rehabilitation should always be the responsibility of the state," he said.